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Dergiler / Turkish Journal of Mathematics and Computer Science / 2018 / Cilt: 8 - Sayı: 8

Quenching for A Nonlinear Diffusion Equation with Singular Boundary Outfluxes

Burhan Selcuk
Nuri Ozalp
Sayfa
65–69
Yayın Tarihi
2022-11-03
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, we show the time derivative blows up at the quenching timeand we also establish results on quenching time and rate for certain nonlinearities.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we study a nonlinear diffusion equation (φ(u))t = uxx, 0 0 with singularboundary outfluxes ux(0, t) = u−p(0, t), ux(a, t) = −u−q(a, t).
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Temel Bulgular & Veri:Firstly, we get the quenching occurs in a finite time atthe boundary x = a under certain conditions.
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Sonuç & Katkı:Finally, we show the time derivative blows up at the quenching timeand we also establish results on quenching time and rate for certain nonlinearities.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, we study a nonlinear diffusion equation (φ(u))t = uxx, 0 0 with singularboundary outfluxes ux(0, t) = u−p(0, t), ux(a, t) = −u−q(a, t). Firstly, we get the quenching occurs in a finite time atthe boundary x = a under certain conditions. Finally, we show the time derivative blows up at the quenching timeand we also establish results on quenching time and rate for certain nonlinearities.

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Bu Makaleye Atıf Yap

Selcuk, B., Ozalp, N. (2022). Quenching for A Nonlinear Diffusion Equation with Singular Boundary Outfluxes. Turkish Journal of Mathematics and Computer Science, Cilt: 8 - Sayı: 8, 65–69. https://ajindex.com/articles/609173

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Kaynakça (9)

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  5. Selcuk, B., Ozalp, N., Quenching for a semilinear heat equation with a singular boundary outflux, Int. J. Appl. Math, 29(4)(2016), 451–464
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  9. Zhi, Y., Mu, C., The quenching behavior of a nonlinear parabolic equation with a nonlinear boundary outflux, Appl. Math.Comput., 184(2007), 624–630.